The sequence `{x_(1),x_(2),…x_(50)}` has the property that for each `k`, `x_(k)` is `k` less than the sum of other `49` numbers. The value of `96x_(20)` is

Options

A. `300`
B. `315`
C. `1024`
D. `0`

Answer

B

Explanation

`(b)` We have `x_(k)+k=S-x_(k)` where `x_(1)+x_(2)+…+x_(k)=S`
`implies2x_(k)+k=S`
`:.2sum_(k=1)^(50)x_(k)+sum_(k=1)^(50)k=sum_(k=1)^(50)S` ,brgt `implies2(S)+(50.51)/(2)=50S`
`implies48(S)=25.51`
`impliesx_(20)=((25.51)/(48)-20)(1)/(2)=(315)/(96)`